A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new tree model, GRST, improves option pricing without log-normality assumptions.
GP-BART improves BART's predictive performance by incorporating Gaussian process priors.
Optimal algorithms learn Gaussian trees and polytrees from data.
BARK optimizes black-box functions using Bayesian Additive Regression Trees.
New MC-Tree method combines Monte Carlo and binomial tree for option pricing and CVA.
Researchers improve tree model recovery from noisy data.
The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the learning rate as the number of samples increases is discussed. Specifically, the error…
Efficiently learns Gaussian tree models with near-optimal sample complexity.
The benefits of diversifying risks are difficult to estimate quantitatively because of the uncertainties in the dependence structure between the risks. Also, the modelling of multidimensional dependencies is a non-trivial task. This paper focuses on one such technique for portfolio aggregation, namely the aggregation o…
This study converts BART to Gaussian process regression, revealing its limitations and potential improvements.
EM algorithm converges to global max in latent Gaussian tree models.
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…
Paper proposes a VB method for TS-SBP mixture models with reduced computational cost.
We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges onto a global solution. The structure learning involves combinatorial operations…
Gaussian latent tree models, or more generally, Gaussian latent forest models have Fisher-information matrices that become singular along interesting submodels, namely, models that correspond to subforests. For these singularities, we compute the real log-canonical thresholds (also known as stochastic complexities or l…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models, hidden Markov models, Gaussian mixture models, and Markov evolutionary trees. The …
We describe various sets of conditional independence relationships, sufficient for qualitatively comparing non-vanishing squared partial correlations of a Gaussian random vector. These sufficient conditions are satisfied by several graphical Markov models. Rules for comparing degree of association among the vertices of…
Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for parameter estimation, inference, and structure learning mainly rely on the Gaussian or…
New method improves stability of Gaussian process approximations.
In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as linear transformations of tree models. This is a new way to decompose the covariance…
Bayesian methods improve drug discovery experiment design.
Robustifies tree learning algorithms for corrupted data.
Consider jointly Gaussian random variables whose conditional independence structure is specified by a graphical model. If we observe realizations of the variables, we can compute the covariance matrix, and it is well known that the support of the inverse covariance matrix corresponds to the edges of the graphical model…
This paper proposes an online tree-based Bayesian approach for reinforcement learning. For inference, we employ a generalised context tree model. This defines a distribution on multivariate Gaussian piecewise-linear models, which can be updated in closed form. The tree structure itself is constructed using the cover tr…
A hybrid model for Bayesian optimization handles mixed variables using MCTS for categorical and GP for continuous.
Tree ensemble kernels improve Bayesian optimization for mixed features and constraints.
A novel stepwise VI method using vine copulas for complex latent dependence.
Dynamic Vine Copulas detect and quantify time-varying higher-order interactions in multivariate systems.
In latent Gaussian trees the pairwise correlation signs between the variables are intrinsically unrecoverable. Such information is vital since it completely determines the direction in which two variables are associated. In this work, we resort to information theoretical approaches to achieve two fundamental goals: Fir…
A new algorithm, Regular Tree Search, tackles non-convex simulation optimization problems.
Regression trees learn gradients of differentiable functions.
In this paper, learning of tree-structured Gaussian graphical models from distributed data is addressed. In our model, samples are stored in a set of distributed machines where each machine has access to only a subset of features. A central machine is then responsible for learning the structure based on received messag…
Combines BART and Gaussian process for spatial covariate prediction with uncertainty.
Algorithm recovers permutations of high-dimensional Gaussian vectors with constant correlation.
Sum-Product Networks (SPNs) can be regarded as a form of deep graphical models that compactly represent deeply factored and mixed distributions. An SPN is a rooted directed acyclic graph (DAG) consisting of a set of leaves (corresponding to base distributions), a set of sum nodes (which represent mixtures of their chil…
A new tree-based model improves uncertainty estimation in sequential optimization.
Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, calle…
CAT method learns causal structure of directed trees efficiently.
Bayesian learning for forests and trees improves graph detection and structure learning.
SMAC method optimizes tree-boosting hyperparameters best.
MSTs provide a fast and meaningful clustering method in low-dimensional data.
New algorithm recovers graph structure from noisy data.
Fairness, through its many forms and definitions, has become an important issue facing the machine learning community. In this work, we consider how to incorporate group fairness constraints in kernel regression methods, applicable to Gaussian processes, support vector machines, neural network regression and decision t…
Efficiently optimizes expensive functions with multi-step lookahead using one-shot optimization.
Improved algorithm for partial recovery of tree-structured graphs with noisy data.
Monte-Carlo Tree Search (MCTS) methods are drawing great interest after yielding breakthrough results in computer Go. This paper proposes a Bayesian approach to MCTS that is inspired by distributionfree approaches such as UCT [13], yet significantly differs in important respects. The Bayesian framework allows potential…
Small neural networks embed arbitrary metric spaces into Gaussian mixtures.
We explore the algebraic structure of the solution space of convex optimization problem Constrained Minimum Trace Factor Analysis (CMTFA), when the population covariance matrix has an additional latent graphical constraint, namely, a latent star topology. In particular, we have shown that CMTFA can have either a …